~ ) Pergamon

Socio-Econ. Plann. Sci. Vol. 29, No. 2, pp. 113-124, 1995 Copyright © 1995 Elsevier Science Ltd

0038-0121(95)00005-4 Printed in Great Britain. All rights reserved 0038-0121/95 $9.50+ 0.00

Provision of Public Services When Private Alternatives Exist

ANN VAN ACKERE London Business School, Sussex Place, Regent's Park, London NW1 4SA, U.K.

Abstract--This paper studies the provision of, and demand for, a public service when a private alternative is available. We link the concept of adequate resources for a public service to the availability of a private alternative, rather than to the public service's ability to meet total demand. We also consider a situation where only part of the population has access to the state service (as is, for instance, the case with subsidised housing) and formalize the concept of the poverty trap, which occurs when access to the public service is of an all or nothing type.

INTRODUCTION

In many countries, some services (or goods) are available free or at low cost from government agencies. Typical examples include health care, public transportation, subsidised housing, and education. It is generally recognized that providing a service at a price below the actual cost leads to overconsumption. This, in turn, may cause congestion of the facilities providing the service, unless these are expanded adequately [6]. The waiting list of the British National Health Service, approaching 1 million people [9], is one example.

We interpret the term congestion in a very broad sense, including queueing, waiting lists and overcrowding. Congestion of the facility causes users to incur non-financial costs in terms of waiting-time (actually standing in line [7] or being on a waiting list [5]) and/or discomfort. These factors are valued differently by different people. Individuals who attach a high price to time, speed of service and comfort react to a situation of congestion by looking for an alternative source of supply, which they usually find in the private sector.

Consequently, there are many situations where a service is available free (or below cost) from the state, while at the same time an equivalent, or possibly better, alternative is offered by the private sector. In many countries, health care is partially or fully paid for by the state. Everyone has to contribute to this system (usually proportionally to one's income), independently of whether or not one uses it. Parallel to this state system, a private health care sector exists in many of these same countries. A second example is transportation. Most countries have a partially subsidised public transport system. This includes mainly trains and buses. The private alternative consists of taking a cab (or one's own car). Subsidised housing differs from the first two examples in that there usually are restrictions as to who qualifies for this benefit, implying a trade-off between the number of housing units available, and their quality in terms of size and comfort. Here, the state must also make an allocation decision.

When both a state run system and a private alternative exist, the following properties can mostly be observed: (1) the financial cost of the private system is higher; and (2) the state system is more expensive in terms of time, delays and lack of comfort. How people value these characteristics depends, among others, on their wealth. The wealthier an individual is, the more value het can attach to time and comfort, as he worries less about the financial aspect.

Our intention here is to analyze how people choose between the public and private alternatives, as a function of their wealth, where wealth is used as a proxy for people's valuation of time and comfort. We show that, when the public service has adequate resources, there exists a critical wealth

t Male form used for sake of convenience

113

114 Ann van Ackere

level such that the more wealthy select the private alternative while the less wealthy select the public service, as is to be expected. In this situation, a number of people who could access the private alternative select the state service. We also show that, when the resources of the public service are inadequate, the individuals with an intermediate wealth level get the worst deal: they find themselves in a position where they cannot afford the available private sector alternative, and are forced to join the state service, adding to the existing overcrowding. It is in those instances that subsidies to enable individuals to use the private service can be most effective: at the margin, a small subsidy may be sufficient to enable an individual use of the private service, making him considerably better off, and reducing congestion in the state facility.

This approach is especially suitable when the private sector is able to provide the service at lower cost. For instance, in the wake of the Los Angeles riots, Becker [2] suggests the use of education-vouchers, which inner city youths could use to gain access to the high school of their choice, to attend trade-school training programs, or to get on-the-job training in the private sector. He states that " . . . m a n y parochial and other private schools provide better education with much smaller expenditures per student, and trade schools usually only spend a fraction of what public schools do. A generous voucher system could cost only half of what is spent by public schools--even less for those in on-the-job and trade-school training programs." (p. 8)

That individuals with intermediate wealth levels are worse off is not a surprise, in view of some of the comments made by Nichols et al. [7]. They point out that when only a public facility with zero money price and private substitutes are available " . . . T h e two extremes of the income distribution are, therefore, probably getting the appropriate choices. The pairings offered, however, have a sharp discontinuity between the zero money price at which the good is fully subsidized by general taxes, and the minimum feasible money-time price pairing which just yields normal profits. . . . The general effect is to serve poorly those with a low but positive marginal product of labour."(p. 321) They conclude that " . . . there may be a high payoff in increased social welfare to ingeniously conceived expansions in the number of waiting time-money price pairings in the public sector." (p. 322).

This idea has been implemented in a number of cases. The best known example is the existence of two (or more) classes on most railway systems: individuals can choose to pay a higher price to benefit from a more comfortable seat in a less crowded carriage. The fact that part of the population is willing to pay extra to avoid crowding for an otherwise identical service is illustrated by the Paris underground system, which for many years charged first and second class fares for identical carriages, with the first class carriages being generally less crowded.

As mentioned above, targeted subsidies may yield similar results. Fundamentally, the choice is between expanding the public service (and making its use more attractive) by increasing the number of congestion-money combinations, or encouraging expansion of the private sector by making it accessible and desirable to a larger fraction of the population.

Cullis and Jones [1] look at a model where a service (hospitalization) is rationed by waiting lists. They state t h a t " . . , the cost of waiting (i.e. the dissipated benefits) can never exceed P . . . " , where P denotes the price of private treatment. They do not consider the situation of individuals whose waiting costs exceed P, but who cannot afford private treatment. For instance, the loss of earnings resulting from an 18 month inability to work while waiting for a hip replacement (the present target of the Patient's Charter [9]) may well exceed the cost of having the procedure performed privately! How well off people in this situation are depends also on whether or not they are able to do without the service. For instance, it is possible to skip the annual check-up at the dentist, but it is more difficult to stay home from work because buses are overcrowded and unreliable.

Ireland [4] studies the mix of social and private provision of goods and services. He focuses on a situation where tax income can be allocated to the social provision of goods and services, to income supplements, or to transferable vouchers (to be used towards the cost of private provision). He points out that social provision affects both the income distribution and the pattern of consumption, and is therefore more than a pure redistribution device. Ireland's model considers the customer's overall utility (individuals allocate their income between the state service or the private alternative (with a choice of quality in the latter case) and a composite commodity), while we focus solely on the net benefit of the specific service being considered.

The situation we discuss is related to club theory (see, for instance Ref. [8]). There are two clubs,

Provision of public services when private alternatives exist I15

one consisting of individuals selecting the state service, and the other of individuals choosing the private alternative. This latter club is able to turn away members, because of the high money price. A system where all individuals must contribute to the provision of the state service through taxation amounts to compulsory membership (but not use) of the state club, which traditional club theory does not deal with.

The paper is structured as follows. In the next section we present the general model. We then discuss a numerical example, and end with some concluding remarks.

THE MODEL

We study a situation where each individual can choose how he wants a specific service to be performed. He can either have the service carried out by a state agency, free of charge (this option will be referred to as the state service), or he can pay for a private company to provide the service. More generally, we can think about the incremental cost of using the private rather than the state service. Each individual is characterized by his (non-negative) wealth level, denoted w, which determines his preferences for money, time, comfort, etc. Wealth is distributed among the population according to some distribution, with cumulative distribution function F(. ) and support [0, o0).

Nichols et al. [7] approximate the cost of time by an individual's wage rate. We prefer to deal with the more abstract concept of wealth, as it accounts for non-wage aspects and relates more closely to taste for non-monetary values. For instance, the definition of what level of discomfort is acceptable to a specific individual depends on the level of comfort he is used to and the available alternatives. This is related to his purchasing power, which is a function not only of his wage, but also of other sources of income, such as interest on savings, legacies, etc.

In general, the private alternative will involve a considerable financial cost, while the state service will be more expensive in terms of time, delays and/or lack of comfort. As noted, individuals value these costs differently, depending on their wealth. The utility of an amount of money m to an individual with wealth w will be denoted by M(m, w).

Assumption I. M(m, w) is continuous, strictly increasing in m and strictly decreasing in w. The continuity assumption is for mathematical convenience. The second part of this assumption

is obvious: more money implies a higher utility. The last part implies that the larger one's wealth, the less value one attaches to a specific sum of money. It is this latter argument which has lead the U.K. to experiment (unsuccessfully) with a system of fines related to disposable income.

The disutility of a waiting time and/or discomfort c to an individual with wealth level w will be denoted T(c, w).

Assumption 2. T(c, w) is continuous and strictly increasing in both c and w. The continuity assumption is again for mathematical convenience. The second part of the

assumption is obvious: greater loss of time and/or greater discomfort means a higher disutility. The last part implies that the larger one's wealth, the higher the value one is able to attach to time and/or comfort.

Consider selecting the private alternative. Let Rp denote the utility derived from having the service performed privately, and let Cp denote the financial cost incurred (e.g. the cost of health insurance or a cab ride) or, more generally, the incremental cost over the state service. Assuming additive utility, the resulting net utility from this service for an individual with wealth w is:

e(w) = Rp - M(Cp, w). (1)

Note that, by Assumption 1, P(w) is strictly increasing and continuous in the wealth level w. Also, P(w) is independent of the decisions of other individuals. Making P(w) dependent on other individuals' decisions (e.g. if more people decide to take a cab, waiting time increases and traffic gets worse) would make the analysis more complex, but does not alter the qualitative conclusions. This assumption is partially motivated by the fact that the private sector typically reacts faster to changes in demand: existing facilities adapt their capacity or new competitors enter the market.

In terms of club theory, the assumption of independence of P(w) on the decisions of other

116 Ann van Ackere

individuals can be motivated by the long-term, equilibrium perspective: fees are used to increase capacity, keeping congestion at a constant level, and keeping the members' utility unchanged.

We assume that there exists a critical wealth level Wp such that individuals with wealth w < wp are denied access to the private alternative. Reasons include the prohibitive cost of a service (e.g. health insurance is too expensive) or an unsatisfactory credit-rating (for instance, uncertain future earnings resulting in the inability to obtain a mortgage). The former situation occurs when the cost of providing the service is such that at least a fraction of the population cannot afford it. This has resulted in the creation of a social security network in many countries. The latter situation is a case of market failure.

Next, consider the alternative of selecting the state service where we let Rs denote the resulting utility. In the special case where the actual service performed is identical under the state service and the private alternative, the equality Rs = Rp holds. The loss of time and the amount of discomfort experienced will depend on the level of congestion, which is determined by the amount of resources available and the number of people using the service. We will assume that the amount of resources is given. Let Cs(W) denote the waiting time and/or loss of comfort resulting from selecting the state service when a fraction F(w) of the population does so. This would be the case, for instance, if all individuals with wealth less than or equal to w selected this alternative. The function cs(w) increases in w. We also assume that this function is continuous. Let S(w', w) denote the net utility an individual with wealth w obtains from selecting the state service when a fraction F(w') of the population does so; i.e.

S(w', w) = Rs- T[c~(w'), w] (2)

By Assumption 2, S(w', w) is continuous, and decreases in both w (the wealth level) and w' (a measure for the congestion of the system). To avoid the uninteresting cases where all individuals always prefer the private service (i.e. no one ever uses the state service), or all individuals always prefer the state service, we make the following assumption:

Assumption 3. P(0) < S(0, 0) and P ( ~ ) > S ( ~ , 0o). These assumptions results in a vertically segmented market [as in case (ii) of Ireland [4]]. We next

define a wealth level which will play a crucial role in stating our results. Definition 1. Let W~p be the wealth level satisfying P(w~p)= S(w~p, Wsp). This definition states that if a fraction F(w~p) of the population selects the state service, then an

individual with wealth W~p is indifferent between the state service and the private alternative. The continuity and strict monotonicity of P ( . ) and S( . , . ) , together with assumption 3, imply that Wsp exists and is unique.

We now state our definition of adequate resources for the state facility, given the availability of private services. We take the viewpoint that the state aims to complement the existing private services (i.e. serve those who fall outside the private service) rather than substitute for it.

Definition 2. For a given level of access to private alternatives, the resources of the state service are said to be adequate whenever W~p ~> Wp. Conversely, the resources of the state service are said to be inadequate whenever Wsp < Wp.

This definition implies that the resources of the state service are considered to be adequate if all individuals who are denied access to the private alternative are better off with the state service than they would be with the private service. In other words, they would not wish to use the private alternative, even if they had access to it; i.e. the state facility and the private service satisfactorily complement each other.

Using these definitions, we can state the following result: Proposition 1. (a) When the resources of the state services are adequate, an individual with

wealth w prefers the state service if w < w~v, the private service if w > wsp, and is indifferent when w = Wsp; (b) When the resources of the state service are inadequate, an individual with wealth w will choose the state service if w < Wp and the private service if w ~> wp.

Proof. This follows immediately from the definitions of wp and w~p, and the monotonicity of P ( . ) and S( . , . ) .

These results are illustrated graphically in Fig. la and lb. For simplicity, the functions S ( . , . ) and P ( . ) are drawn as linear equations. This does not affect the qualitative results, as can be seen from the numerical example, below. The horizontal axis represents wealth levels and the

Provision of public services when private alternatives exist 117

(a)

P(w)

I I I I

Wp Wsp

S(Wsp,W)

S(w,w)

W

(b)

i I I

I

I (wp ,w) I I I ~ S (w,w) I i

W ~ W s p Wp

Fig. la,b. Unlimited access to the state service.

W

vertical axis net utility derived from the service. Figure I a represents the case of adequate resources for the state service (Wp ~ Wsp). The bold line indicates the individuals' choice. Individuals with wealth w < Wsp prefer the state alternative. Their net utility equals S(wsp, w) = R~ - T[c~(W~p), w]. Individuals with wealth w > W~p prefer the private alternative. Their net utility equals P(w) = R p - M(cp, w). Individuals with wealth w = wsp are indifferent. Their net utility equals S(wsp, W~p) - P(w~p). All inviduals can afford the alternative they favour. Note that the individuals with wealth levels wp ~< w < Wsp prefer the state service, although they can access the private alternative.

Figure Ib pictures the case of inadequate resources. Here, W~p < Wp. Individuals with w/> Wp select the private alternative and obtain a net utility equal to P(w) = Rp - M(cp, w). Individuals with wealth w < Wp must use the state service. The utility of customers of the state facility equals only S(wp, w) since individuals with wealth wsp < w < wp are forced to select the state service, thus increasing congestion. In this case, individuals who select the state service would be better off with the private alternative, but are denied access to it. It is in this latter situation that incentives to use the private alternatives (e.g. tax credits, low interest loans, etc.) will have the largest impact on overall welfare. For instance, in Fig. l b, a subsidy equivalent to Wp- w' is sufficient to increase the utility an individual with wealth w' derives from this service to

118 Ann van Ackere

R p - M[cp- (Wp- w'), w'] > P(W'), an increase exceeding the amount a indicated on the figure. There is also an indirect welfare effect, due to the decreased congestion in the state system.

Webb and Willcox [10] discuss the impact of the U.K. Right to Buy policy, enabling council tenants to buy their own property, often at substantial discounts. They point out that it is mostly the better-off tenants who exercise this right (i.e. in our model, those whose wealth is close to Wp). Income generated from these sales can be re-invested in additional accommodation. In this example, self-selection among tenants enables the state to target subsidies (the discounts on house prices) to those individuals who are most keen to enter the private housing market. Indirect benefits result from the ability to invest the proceeds in new housing developments.

We have thus far assumed that everybody has access to the state facility. In some instances, access to this service is restricted to individuals whose wealth level is below a certain threshold w~. This is typically the case for subsidised housing. The available resources can either be used to build a small number of high quality housing units to accommodate a small fraction of the population (w s low), or a larger number of less spacious, less comfortable units (ws high). One instance of this conflict of interests can be found in Gardiner and Hills' [3] discussion of local authorities' voluntary transfer of their housing stock to newly formed non-profit, non-public sector, housing associations. In several cases, councils have passed on the capital receipts of the sales to these associations to build new housing units. If the transfer units receive a low valuation, the existing tenants can confidently expect low rents and charges, as the housing association faces a lower debt burden. On the other hand, potential future tenants prefer a high valuation, as this means larger building programmes, which benefits those who would otherwise be unable to gain access to this low-price accommodation.

Let us first consider the case of sufficient resources. (w o ~< W~p). Three cases occur, depending on the relative magnitudes of w~, wp and W~p. If w~ > W~p, this new constraint is non-binding, and the situation remains as in Fig. la. Figures 2a and b shows the remaining two cases.

If Wp < Ws < W~p, individuals with w ~< ws are better off, at the expense of individuals with wealth in the range w~ < w < W~p. As shown in Fig. 2a, this latter group is now forced to use the private service. It is interesting to compare this situation to Fig. 1 b. Here, an individual with wealth level w' is willing to pay any price m satisfying M(m, w') < a to gain access to the state service. Assuming that all individuals with wealth w~ < w < w' do so, this would yield him a utility level S(w', w') - M(m, w')P(w'). His increase in utility would come at the expense of individuals with wealth w < Ws, unless these payments are used to increase state capacity. Alternatively, an individual with wealth w~ would be ill-advised to gain a slight wealth increase, as this would be more than offset by the loss of utility b resulting from being excluded from the state service. This situation is the consequence of an all or nothing policy with respect to access to the public service, and is often referred to as the "poverty trap." One such example is discussed in Webb and Willcox [10] as the "unemployment trap." Families eligible for income support (or benefit units) receive assistance with their mortgage interest cost if the unit does not contain a full-time worker (defined as working 16 or more hours per week). They provide an example where a couple with a £70 per week mortgage is better off out of work than with one of them earning £10,000 a year.

An extreme case, shown in Fig. 2b, occurs when ws < Wp. Again, individuals with w ~< w~ are better off, at the expense of those with w~ < w < Wsp, while individuals with wealth Wp ~< w < wsp are forced to use the private service. But, individuals with w~ < w < Wp are in the unenviable position of being denied access to both the public and private services, and would end up homeless in the housing example. This problem could be resolved by pulling away resources from individuals with wealth w < w~ (increasing w~ to the level of Wp) or by devising a support mechanism that would make the private service accessible to this group. This is an extreme illustration of the point made by Nichols et al. [7], that individuals at the extremes of the wealth distribution are getting the appropriate choice, but those in the middle are not.

The poverty trap facing individuals with wealth ws is illustrated here in an extreme way. Unless one can jump (at least) to wealth level Wp, it is considerably better to stay at w~! In the Webb and Willcox [10] example, taking a £10,000 per year job would result in the loss of help with mortgage interest payments, which could lead to arrears and ultimately repossession.

Next, let us consider the case of insufficient resources. For w~ 1> w~, the situation is unchanged. Figure 3 shows the case w~ < Wp. Again, individuals with w~ < w < Wp are excluded from both

Provision of public services when private alternatives exist 119

(a)

S(Ws'W) P(w)

S(w,w)

I I I I I I

i V Wp w s w' Wsp

W

(b)

S(w s ,w) ~ P ( w )

I I

I I

.I I

!

w s Wp Wsp

Fig. 2a,b. Limited access to the state service, sufficient resources.

W

services. This situation has some similarity with Fig. lb, as an individual with wealth w' would derive a considerable benefit from any arrangement that would enable him to gain access to the private service.

These two cases can be thought of as a "reversed poverty trap". With the poverty trap, a small increase in wealth leads to being considerably worse off. Here, a small decrease in wealth (falling below wp) leads to being considerably worse off. One could consider the case of an individual who gets behind with mortgage payments due to a raise in interest rates, and whose house is repossessed. He then finds himself put up in a "bed and breakfast" by the local authorities (Fig. l b) or homeless (Fig. 3).

A N U M E R I C A L EXAMPLE

In this section, we present a numerical example that illustrates the main points of the previous section, and allows us to carry out some sensitivity analysis. We make the following assumptions:

- -Wea l th follows a triangular distribution on the interval [0,1], with mode m. Initially, we assume a symmetric distribution (rn = 0.5).

120 Ann van Ackere

- -Conges t ion costs in the state facility equal cs(w)= F(w) / [ l - F(w)]; i.e. they increase at an increasing rate.

- - W h e n a fraction F(w') of the population elects to use the state service, congestion costs equal T[cs(w'), w] = wc~(w') for an individual with wealth w. Note that this implies as an extreme case that an individual with zero wealth is not sensitive to congestion.

- - A n individual with wealth w incurs a disutility M(cp, w) = Cp/W from paying Cp to use the private facility. This implies that an individual with zero wealth would incur an infinite disutility.

Initially we assume that both facilities deliver identical service. Further, let Rp = R~ = 10. We also let cp = 2, which implies that if no state service is available, all individuals with wealth level w >~ 0.2 (i.e. 92% of the population in the base case) expect positive benefits from using the private service.

Figure 4a illustrates this base case: w~p = 0.69, and 81% of the population uses the state service if w~ ~< w~p. What if resources are insufficient, e.g. wp = 0.75 (i.e. only 12.5% of the population has access to the private service)? Individuals with wealth in the interval [0.69, 0.75] switch to the state service. The shaded area in Fig. 4b provides an idea of the magnitude of the loss of utility resulting from this shift. Note that this area is not an exact measure of the total loss of utility, as we do not assume a uniform wealth distribution.

What is the impact of increasing the state facility's resources so as to achieve a 50% reduction in congestion costs; i.e. cs(w) = 0.5 x F(w)/[1 - F(w)]? As shown in Fig. 4c, the curve S(w, w) moves outwards, and w~p now equals 0.75, implying that 87.5% of the population chooses the state service, compared to 81% in the base case. In other words, over one third of the individuals who used the private service have switched to the state service.

Next, let us consider what happens if the wealth distribution is skewed to the right (e.g. m = 0.2). This implies that there are considerably more individuals at the lower end of the distribution than at the high end, a more realistic assumption than the symmetric distribution used in the base case. Figure 4d shows that wso = 0.63, implying that if enough resources are available (Wp < 0.63), 83% of the population will use the state service. Figure 4e illustrates the case of insufficient resources. I f Wp = 0.75, only 8% of the population is able to use the private service (compared to 17% when there are sufficient resources, a reduction of over 50%). The shaded area again provides some idea of the magnitude of the loss of utility.

What if the private service is valued more highly than the state service? Let us return to the base case, and assume a 20% increase in the value of the private service (Rp = 12). Figure 4f shows the resulting situation: Wsp = 0.60, implying that, if Wp ~< Wsp, 31% of the population uses the private service, compared to 19% in the base case. Imposing the constraint wp = 0.75 yields Fig. 4g: as in the base case (Fig. 4b), only 12.5% of the population can access the private service. Once again, the shaded area provides some idea of the magnitude of the loss of utility.

S )

/ , s p w Fig. 3. Limited access to the state facility, insutticient resources.

Provision of public services when private alternatives exist 121

(a) 10

2

p(w)

S(Wsp ,w)

w

0.2 0.4 0.6Ws p 0.8 1

(b)

S(Wp ,w)

S(Wp,W)

2

w

0 0.9. 0 .4 0 .6 0 .0 1 Wsp Wp

SEPS 29/2--D

(c) 10

8

6

4~

~ p(w)

f 1 / . . . . t 7w

0 0.2 0.4 0.6 wspO.8 t

Fig. 4a-c. Caption on p. 123.

,w)

(d) 10

0 . 2 0 . 4 0 . 6

122 Ann van Ackere

p(w)

I

S(Wsp,W)

w 0.8 1

Wsp

(e) 10

8

6

4

2 i

,< I

i | |

0.2 0 . 4 0.6 Wsp

._.....____~,- p(w)

~ ' ~ , ~ , S(Wsp ,w)

S(Wp,W)

~, , w

0.8 1 w

P

(f) 10

4

2

p(w)

Wsp ,w)

/ 1 t , , | , W

0.2 0 . 4 O.i 0 . 8 l Wsp

Fig. 4d-f. Caption opposite.

Provision of public services when private alternatives exist 123

(g) 10 8

6

4

2

~ p(w)

S(Wsp

|

0 . 2 0 . 4 0.6

w sp

,w)

~ S(Wp,W) I I s(w,w) I ~ , w

0.8 1 w P

Fig. 4a g. A numerical example.

C O N C L U S I O N S

Our aim in this paper was to study the provision of a public service, when a private alternative exists. We suggested a definition of adequate resources for the public service, linking this concept to the availability of a private alternative: the state aims to complement the private service. Our analysis confirms the findings of previous work, which indicate that while individuals at the extremes of the wealth distribution get appropriate choice, this is not so for the middle group.

We also formalized the concept of the "poverty trap", which arises when individuals whose wealth level exceeds a certain threshold are excluded from the public service: a marginal increase in wealth may leave them considerably worse off, even if they have access to the private service. We introduced the concept of a "reversed poverty trap," which arises when individuals whose wealth level falls below a certain threshold are excluded from the private service. A slight decrease in wealth leaves them considerably worse off, even if they have access to the state service.

We alluded to the policy dilemma earlier in the introductory section: expanding the public service versus encouraging the private sector. Comparing Fig. l b and 3, both of which reflect insufficient resources, can help us assess the appropriateness of these two approaches. As previously argued, in Fig. lb the subsidy required to enable individuals with wealth levels close to Wp to access the private service is small compared to the benefit they derive. In addition, this would make those who remain in the public sector better off. Therefore, enabling individuals to move from the public to the private sector is beneficial.

Next, consider Fig. 3, and let us focus on individuals in the interval (w~, wp), who are presently excluded from both the state and private sectors. These individuals would favour being allowed to access the state service, although a subsidy enabling them to access the private sector would be an even larger improvement. For individuals close to w v this latter option is likely to be considerably less costly from the state's perspective. As a concrete example, it is a choice between the state building additional low-rent housing, and giving people a housing allowance (i.e. paying part of their rent). A combination of both options may be desirable: build housing for those with a wealth level close to ws while providing an allowance to those close to w~. Either measure leads to a situation as represented in Fig. lb. Moving to Fig. la (i.e. removing the reversed poverty trap), requires either bringing down wp (i.e. increasing access to the private service: housing subsidies, tax rebates for health insurance, etc.) or increasing Wsp (i.e. additional resources to the state sector).

Next, consider Fig. 2b. Although there are sufficient resources (Wsp > Wp), they are focused on a small group of the population (w < ws). Again, a combination of increased access to the state service, and subsidies to enable access to the private sector, is required. Note that here the individuals concerned would favour access to the state service vs access to the private service. Either measure leads to a situation as represented in Fig. 2a: individuals in the interval (w~, w~p) have

124 Ann van Ackere

access to the private service, but would be better off with wealth below ws and access to the state service, i.e. they face the poverty trap. As argued before, moving from wealth level ws to a slightly higher wealth level results in being considerably worse off.

The first priority should therefore be to remove this "discontinuity," i.e. move from Fig. 2a to Fig. la. One option here consists of removing the limit ws, i.e. spread the available resources of the state sector over a larger number of people. This is done at the expense of individuals with wealth levels below w s. Such an undesirable side-effect can be offset to some extent by requiring individuals in the range (Ws, Wsp) to contribute to the cost of the state service.

A less radical option would be to focus on decreasing the size of the "gap," for instance by providing a housing allowance to individuals in the range (w~, wsp). This would reduce the difference between S(ws, ws) and P(w~), i.e. b in Fig. 2a. The allowance should decrease as wealth increases, but not on a £ for £ basis, as this would remove the incentive to take on a job, or work overtime. Again, a combination of both options may be most desirable.

Ideally, one would like S(w~p, w) in Fig. la to be horizontal (if not slightly increasing): efforts to increase one's wealth, i.e. accepting a job or working overtime should not be penalized. This could be achieved by having the state sector offer a range of service levels, at increasing cost, at least up to the congestion--price combination at which the private sector becomes viable. The revenue raised in this way could then be allocated to improve the state service. One such example is the patient's daily contribution to the cost of a hospital stay in Belgium. Patients receive identical care, but their daily contribution depends, among others, on whether they elect to stay on a ward, share a double room, or occupy a single room.

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